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Krull dimension of skew-Laurent extensions

1984; Mathematical Sciences Publishers; Volume: 114; Issue: 1 Linguagem: Inglês

10.2140/pjm.1984.114.109

1945-5844

Kenneth Goodearl, T. H. Lenagan,

Commutative Algebra and Its Applications

A precise formula is derived for the (noncommutative) Krull dimension of a skew-Laurent extension R[Θ^\... ,θ* λ \ 9 where R is a commutative noetherian ring of finite Krull dimension, equipped with u commuting automorphisms σ,,... ,σ M .The formula is given in terms of heights and automorphian dimensions of prime ideals of R, where the automorphian dimension of a prime ideal P is a positive integer that measures the invariance of P relative to products of powers of the σ, .As part of the development of this formula, the Krull dimension of a skew-Laurent extension Rlθ^1] over a right noetherian ring R of finite right Krull dimension is determined.Also, some partial results are obtained for an iterated skew-Laurent extension R[θ^ \... ,0* ι ] over a right noetherian ring R of finite right Krull dimension.In particular, a criterion is derived that indicates when such an iterated skew-Laurent extension can achieve the maximum possible Krull dimension.